Related papers: Universal low-energy behavior in three-body system…
The cosmological constant $\Lambda$ is a measure of the energy density of the vacuum. Therefore properties of the energy of the system in the metastable vacuum state reflect properties of $\Lambda = \Lambda(t)$. We analyze properties of the…
We present an exact solution of a 1D model: a particle of incident energy $E$ colliding with a target which is a 1D harmonic ``solid slab'' with $N$ atoms in its ground state; the Hilbert space of the target is restricted to the ($N+1$)…
We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and…
We consider a $d$-dimensional gas in canonical equilibrium under pairwise screened Coulomb repulsion and external confinement, and subject to a volume constraint. We show that its excess free energy displays a generic third-order…
We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $\rho\to 0$, the ground state energy density satisfies $$e_0(\rho) =…
It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature $\Xi$ and the critical temperature $T_c$ is (approximately) given by a universal constant, independent of the microscopic details of the…
Particles with short-range interactions and a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-body sector, the universal…
The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point…
Understanding how quasi-particles interact with impurities is crucial for unveiling novel properties of quantum many-body systems. A prominent example is the enhanced scattering between electrons and magnetic impurities in the low-energy…
Atom-dimer scattering below the three-body break-up threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly-bound three-body state are shown to be strongly correlated.…
We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum,…
Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state…
We prove that for a single-component many-body system at zero temperature the inequality $E_{\rm int} \leq\, P\,V$ holds, where $E_{\rm int}$ is the interaction energy, $P$ is pressure and $V$ is volume. This inequality is proven under…
We determined perturbatively the low-energy universal thermodynamics of dilute one-dimensional bosons with the three-body repulsive forces. The final results are presented for the limit of vanishing potential range in terms of…
When a two-body system is bound by a zero-range interaction, the corresponding three-body system -- considered in a non-relativistic framework -- collapses, that is its binding energy is unbounded from below. In a paper by J.V. Lindesay and…
Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy…
A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass $m$ and the third particle of the mass $m_1$ in the zero-range limit of the interaction between different particles is given…
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…
We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of…
An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze…